Quantum Computing with Trapped Ions

Lange, Wolfgang

doi:10.1007/978-1-4614-1800-9_149

Wolfgang Lange²

1214 Accesses
1 Citations

Article Outline

Glossary

Definition of the Subject

Introduction

Ion Trap Technology

Ions as Carriers of Quantum Information

Laser Cooling and State Initialization

Single‐Ion Operations

State Detection of Ionic Qubits

Two-Qubit Interaction and Quantum Gates

Decoherence

Quantum Algorithms

Distributed Quantum Information with Trapped Ions

Future Directions

Bibliography

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Abbreviations

Ion trap:: Device used for confining charged particles to a small volume of space. There are two types of ion traps: in a Paul trap, the confinement is achieved by using an electric quadrupole radio‐frequency field, while a Penning trap uses a static electric quadrupole field and a static magnetic field. For the right field parameters, the charged particles can be stored in the trapping volume permanently.
Lamb–Dicke regime:: Describes the conditions for strong confinement of ions. In the Lamb–Dicke regime, ions are confined to a region smaller than the wavelength of the optical transition of the ion. Another property of ions in this parameter range is that the ion's recoil energy is less than the energy of a single quantum of vibration in the trap. This suppresses spontaneous sideband transitions. The Lamb–Dicke regime is essential for the reliable operation of laser‐induced quantum gates in an ion-trap quantum computer.
Qubit:: The unit of quantum information processing. A contraction of quantum bit, the term qubit designates quantum system with two quasi-stable states carrying the quantum equivalent of binary information (“0” or “1”). In an ion-trap quantum computer, two long-lived electronic states are employed as quantum memory. Their wavefunctions are represented here by the symbols \( { |g\rangle } \) and \( { |e\rangle } \). The qubit states are manipulated by means of laser pulses.
Quantum register:: A collection of qubits forms a quantum register. The power of a quantum computer increases exponentially with the size N of the quantum register, since in this case \( { 2^N } \) numbers can be processed in parallel. In ion traps, the largest quantum register implemented so far has size \( { N=8 } \).
Normal modes:: The motion of ions in a linear string is strongly coupled due to their Coulomb repulsion. The system can still be described by analogy with a set of independent harmonic oscillators, when collective modes of motion are considered, in which all ions oscillate in phase and at the same frequency. These are called normal modes. A linear string of N ions has N normal modes of axial vibration. Each mode has a characteristic distribution of motional amplitudes for the ions. In the lowest frequency mode, all ions oscillate at the same amplitude, so that the string moves like a rigid body.
Phonon bus:: Since all ions participate in the collective motion, it can be used to transfer quantum information between ions in the string. To this end, each normal mode is considered as a quantum mechanical oscillator, in which quanta of vibrational motion (phonons) can be excited or de‐excited. By coupling their excitation to transitions of the ion-qubit, the phonons serve as a quantum data bus to other ions. Reliable transfer requires that the phonons are restricted to a binary system. The state with no vibrational excitation encodes the qubit \( { |0\rangle } \), one quantum of vibration corresponds to \( { |1\rangle } \).
Rabi‐oscillations:: The term describes the change of state of a two-level atom, induced by the coherent excitation with a laser beam close to resonance.After half a period (phase π), the population is completely transferred, after another half period it is returned to the initial distribution again. By choosing suitable phases, amplitudes, detunings and duration of the pulses, the individual qubits may be manipulated in a fully controlled way and quantum gates between different ions may be induced (via the phonon bus).
Coherent superposition:: According to the laws of quantum mechanics, a qubit can be in an arbitrary superposition of the two basis states with complex amplitudes α and β, written as \( { \alpha |g\rangle + \beta |e\rangle } \). The relative phase is important, for example, \( { |g\rangle-|e\rangle } \) and \( { |g\rangle+|e\rangle } \) are distinct superposition states. As long as a well‐defined phase is preserved, the qubit is in a coherent superposition. This is a precondition for quantum information processing.
Decoherence:: Any loss of coherence of a quantum state is called decoherence.There are many sources of decoherence. In an ion-trap quantum processor, they range from spontaneous decay of the qubit‐levels to phase shifts in fluctuating ambient fields. A quantum computation can only proceed reliably while decoherence is negligible. Quantum error correction is a way to counteract decoherence.
Entanglement:: Entanglement is one of the most important properties of quantum systems and has no classical analogue. A composite system, for example two qubits, is entangled if the states of the individual particles cannot be separated and regarded as independent. Instead, there are strong non-local links between the components, resulting in quantum correlations and state changes of one partner upon measurement of the other. Entangled states have many applications, from spectroscopy to quantum networking. Up to eight ions have been entangled in a deterministic way.
Quantum network:: A system of either local or distant nodes performing quantum calculations and exchanging results via transport of ions or via photon links. Setting up the latter requires a controlled exchange of quantum data between ions and photons, providing flying qubits. The goal is distributed entanglement, for example to transfer qubits over long distances via teleportation and eventually to perform distributed quantum computation.

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Wolfgang Lange

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Lange, W. (2012). Quantum Computing with Trapped Ions . In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_149

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